Determinant Maximization with Linear Matrix Inequality Constraints
SIAM Journal on Matrix Analysis and Applications
Filtering for Texture Classification: A Comparative Study
IEEE Transactions on Pattern Analysis and Machine Intelligence
The FERET Evaluation Methodology for Face-Recognition Algorithms
IEEE Transactions on Pattern Analysis and Machine Intelligence
Sparse Image Coding Using a 3D Non-Negative Tensor Factorization
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
A Riemannian Framework for Tensor Computing
International Journal of Computer Vision
Learning low-rank kernel matrices
ICML '06 Proceedings of the 23rd international conference on Machine learning
Clustering with Bregman Divergences
The Journal of Machine Learning Research
Information-theoretic metric learning
Proceedings of the 24th international conference on Machine learning
Pedestrian Detection via Classification on Riemannian Manifolds
IEEE Transactions on Pattern Analysis and Machine Intelligence
Robust Face Recognition via Sparse Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Region covariance: a fast descriptor for detection and classification
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part II
Just relax: convex programming methods for identifying sparse signals in noise
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
IEEE Transactions on Information Theory
Gabor-Based Region Covariance Matrices for Face Recognition
IEEE Transactions on Circuits and Systems for Video Technology
Fast Pedestrian Detection Using a Cascade of Boosted Covariance Features
IEEE Transactions on Circuits and Systems for Video Technology
An introduction to kernel-based learning algorithms
IEEE Transactions on Neural Networks
ECML PKDD'11 Proceedings of the 2011 European conference on Machine learning and knowledge discovery in databases - Volume Part III
Advances in matrix manifolds for computer vision
Image and Vision Computing
Sparse coding and dictionary learning for symmetric positive definite matrices: a kernel approach
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part II
Local log-euclidean covariance matrix (L2ECM) for image representation and its applications
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part III
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Sparse representation of signals has been the focus of much research in the recent years. A vast majority of existing algorithms deal with vectors, and higher-order data like images are usually vectorized before processing. However, the structure of the data may be lost in the process, leading to poor representation and overall performance degradation. In this paper we propose a novel approach for sparse representation of positive definite matrices, where vectorization would have destroyed the inherent structure of the data. The sparse decomposition of a positive definite matrix is formulated as a convex optimization problem, which falls under the category of determinant maximization (MAXDET) problems [1], for which efficient interior point algorithms exist. Experimental results are shown with simulated examples as well as in real-world computer vision applications, demonstrating the suitability of the new model. This forms the first step toward extending the cornucopia of sparsity-based algorithms to positive definite matrices.